The digital signal from the sensor consists of long (70uS) and short (28uS) pulses. Timing is critical, so interrupts are disabled by the library (you are using the DHT library, yes?).
Also, noise could be an issue with that protocol. You have a low for a period, then a high for a period - the period of that high, up until it goes low, is what determines if it's a 0 or a 1. If you get a bit of noise, that period could be measured wrongly.
If it is the PWM signal inducing noise, you could try to counter it by reducing the pull-up resistor on the data line to say 4.7K?. You could also try ensuring that your PWM signal is as far away from the data line as practicable.